Practice your algebra skills with this worksheet focused on simplifying expressions using the distributive property and combining like terms.

Sure! Let’s solve each problem step by step using the Distributive Property and then Combine Like Terms as instructed.

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1.) -4(3x - 3) + 9(x + 1)

Step 1: Distribute
- -4 × 3x = -12x
- -4 × (-3) = +12
- 9 × x = 9x
- 9 × 1 = 9

→ Expression becomes:
-12x + 12 + 9x + 9

Step 2: Combine like terms
- x terms: -12x + 9x = -3x
- constants: 12 + 9 = 21

✔ Final Answer: -3x + 21

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2.) -9x[5x + 4] + 10(x + 3)

*(Note: The brackets here are likely just grouping — same as parentheses.)*

Step 1: Distribute
- -9x × 5x = -45x²
- -9x × 4 = -36x
- 10 × x = 10x
- 10 × 3 = 30

→ Expression becomes:
-45x² - 36x + 10x + 30

Step 2: Combine like terms
- x terms: -36x + 10x = -26x
- constants: 30 (no other constants)
- x² term: -45x² (no other x² terms)

✔ Final Answer: -45x² - 26x + 30

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3.) n(1 + 10n) - n(4n - 3)

Step 1: Distribute
- n × 1 = n
- n × 10n = 10n²
- -n × 4n = -4n²
- -n × (-3) = +3n

→ Expression becomes:
10n² + n - 4n² + 3n

Step 2: Combine like terms
- n² terms: 10n² - 4n² = 6n²
- n terms: n + 3n = 4n

✔ Final Answer: 6n² + 4n

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4.) -2n(-8n - 10) - 6(-10n - 3)

Step 1: Distribute
- -2n × (-8n) = +16n²
- -2n × (-10) = +20n
- -6 × (-10n) = +60n
- -6 × (-3) = +18

→ Expression becomes:
16n² + 20n + 60n + 18

Step 2: Combine like terms
- n terms: 20n + 60n = 80n
- constants: 18
- n² term: 16n²

✔ Final Answer: 16n² + 80n + 18

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5.) 8(-4x - 7) + 3(9 - 9x)

Step 1: Distribute
- 8 × (-4x) = -32x
- 8 × (-7) = -56
- 3 × 9 = 27
- 3 × (-9x) = -27x

→ Expression becomes:
-32x - 56 - 27x + 27

Step 2: Combine like terms
- x terms: -32x - 27x = -59x
- constants: -56 + 27 = -29

✔ Final Answer: -59x - 29

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6.) 9(3 - 10n) - 3(10n + 1)

Step 1: Distribute
- 9 × 3 = 27
- 9 × (-10n) = -90n
- -3 × 10n = -30n
- -3 × 1 = -3

→ Expression becomes:
27 - 90n - 30n - 3

Step 2: Combine like terms
- n terms: -90n - 30n = -120n
- constants: 27 - 3 = 24

✔ Final Answer: -120n + 24

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7.) -4(1 - 8x) - 9(-10x - 1)

Step 1: Distribute
- -4 × 1 = -4
- -4 × (-8x) = +32x
- -9 × (-10x) = +90x
- -9 × (-1) = +9

→ Expression becomes:
-4 + 32x + 90x + 9

Step 2: Combine like terms
- x terms: 32x + 90x = 122x
- constants: -4 + 9 = 5

✔ Final Answer: 122x + 5

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8.) -9x(-9 + 6x) - 5x(7 + 4x)

Step 1: Distribute
- -9x × (-9) = +81x
- -9x × 6x = -54x²
- -5x × 7 = -35x
- -5x × 4x = -20x²

→ Expression becomes:
81x - 54x² - 35x - 20x²

Step 2: Combine like terms
- x² terms: -54x² - 20x² = -74x²
- x terms: 81x - 35x = 46x

✔ Final Answer: -74x² + 46x

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9.) -4(n + 6) + (1 + 2n)

*(Note: The “+ (1 + 2n)” is already simplified — no distribution needed for the second part.)*

Step 1: Distribute
- -4 × n = -4n
- -4 × 6 = -24
- Second part: +1 + 2n

→ Expression becomes:
-4n - 24 + 1 + 2n

Step 2: Combine like terms
- n terms: -4n + 2n = -2n
- constants: -24 + 1 = -23

✔ Final Answer: -2n - 23

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10.) -2[x + 9] - 4x[3 - 2x]

Step 1: Distribute
- -2 × x = -2x
- -2 × 9 = -18
- -4x × 3 = -12x
- -4x × (-2x) = +8x²

→ Expression becomes:
-2x - 18 - 12x + 8x²

Step 2: Combine like terms
- x terms: -2x - 12x = -14x
- constants: -18
- x² term: 8x²

✔ Final Answer: 8x² - 14x - 18

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## ✔ Final Answers Summary:

1. -3x + 21
2. -45x² - 26x + 30
3. 6n² + 4n
4. 16n² + 80n + 18
5. -59x - 29
6. -120n + 24
7. 122x + 5
8. -74x² + 46x
9. -2n - 23
10. 8x² - 14x - 18

Let me know if you’d like to see any step explained in more detail!